Systems for treatment planning with overcorrection

ABSTRACT

Orthodontic systems and related methods are disclosed for designing and providing improved or more effective tooth moving systems for eliciting a desired tooth movement and/or repositioning teeth into a desired arrangement. Methods and orthodontic systems include the generation of an overcorrection in the tooth-receiving cavities of an appliance worn in the dentition. The overcorrection may provide an improved and more accurately applied force or moment applied to a tooth. The overcorrected force or moment can move a tooth closer to a desired position than if not overcorrected as sufficient force can still applied to the tooth as it gets closer to the desired position. The overcorrected force or moment may also better target the root of the tooth where the biological response to tooth movement occurs. The overcorrection may be calculated in various ways as described herein.

CROSS-REFERENCE

This application is a continuation of U.S. application Ser. No.15/051,364, filed Feb. 23, 2016, which claims the benefit of U.S.Provisional Application No. 62/119,724, filed Feb. 23, 2015, and U.S.Provisional Application No. 62/119,759, filed Feb. 23, 2015, thedisclosures of each of which are incorporated herein by reference intheir entirety.

BACKGROUND

Prior methods and apparatus for aligning teeth can be less than ideal inat least some instances. While braces can be used to move teeth intoalignment, braces can be cumbersome to wear and can require expertise toplace on the subject. Also, complex movements can be difficult toachieve and orthodontic placement may less than ideally address thecomplex movements of several teeth in at least some instances.

Transparent shell appliances have been used to successfully move teeth.For example, a user can be provided with a series of transparent shellappliances. Each shell of the series of shells may correspond to a stageof the treatment. For example, a fourth shell in a series of ten shellsmay correspond to the fourth state of treatment. Although transparentshell appliances can be used to successfully reposition teeth, thetransparent shell appliances can provide less than ideal results in atleast some instances. For example, complex movements of teeth, such asto fill an extraction can be difficult to treat with transparent shellappliances. Also, in at least some instances, a wearer of a transparentshell appliance may not complete treatment, for example when teeth donot move sufficiently with the appliance and the user stops treatment.Additionally, in at least some instances, the course of treatment mayneed to be reevaluated as the treatment is implemented, which maynecessitate the manufacture of a second series of transparent shellappliances, prolonging treatment time.

Prior methods and apparatus of aligning teeth with transparent shellappliances can rely on providing shells with cavities shaped to thetooth profile at a final intended position and orientation at a stage ofthe treatment. Work in relation to embodiments suggests cavities shapedto position a tooth at a final intended position and orientation at astage of the treatment can provide less than ideal movement. Althoughattachments can be placed on teeth to facilitate movement of the teethwith polymeric shell appliances, the resulting movements can be lessthan ideal in at least some instances. For example, the force applied tothe tooth can decrease as the tooth moves toward the target position.Also, the movement of a tooth may not be uniform, and the tooth may movemore easily along some dimensions than others. For example, the movementof a tooth can occur along six degrees of freedom, and relative movementcompared to a target movement can differ among the degrees of freedom ofthe tooth. Further, the movement of teeth can be coupled, such thatmovement of a first tooth can affect movement adjacent teeth.

Prior appliances to move teeth may provide teeth receiving cavities atlocations corresponding to the locations of the teeth at the end of eachstage of treatment. This approach can be less than ideal in at leastsome instances.

Although manufacturing appliances in accordance with target positions ofthe teeth at the end of each stage of treatment can be effective, workin relation to embodiments suggests that the amount of force applied toeach tooth can be less than or greater than would be ideal, and thecorresponding movement of the tooth can be less than ideal in at leastsome instances. There can be a discrepancy between the locations of theteeth receiving cavities of the polymeric shell appliance applied andcurrent positions of the teeth. The force and moment may be created fromthe deformation of the polymeric shell appliance put on the teeth. Whena tooth is moved close to its position in the next stage of thetreatment course, the discrepancy between the polymeric shell applianceused and the tooth also can get smaller. Accordingly, the force appliedby the polymeric shell appliance can be also reduced. When the force issmall enough, there may be no tooth movement achieved until the nextpolymeric shell appliance with a new, larger discrepancy is used.Additionally, the force and moment created by the polymeric shellappliance can be from the discrepancy of the crown part of the tooth,and may be applied on tooth crown only, for example. However, thebiological response for tooth movement can be generally centered on thetooth root and not the crown. Therefore, the force from the crowndiscrepancy may be less than ideal for root movement.

In light of the above, it would be desirable to provide improved methodsand apparatus for moving teeth to target positions with polymeric shellappliances. Ideally such methods and apparatus would more accuratelymove teeth to target positions with decreased forces.

SUMMARY

Described herein are embodiments of systems and methods to generatemodified, overcorrected positions for a set of appliances such aspolymeric shell appliances. An “achievement matrix” may be generated bydata analysis of past treated cases to generate the modified,overcorrected positions. Alternatively or in combination, a “forcemoment matrix” may be generated by measuring the force and moment fromthe discrepancy of a particular polymeric shell appliance from the teethof a subject. Alternatively or in combination, a rotational componentmay be added to the pure translation movement of a particular polymericshell appliance to compensate for the tipping effect while moving teeth.

Other objects and features of the present invention will become apparentby a review of the specification, claims, and appended figures.

INCORPORATION BY REFERENCE

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each individual publication, patent, or patent application wasspecifically and individually indicated to be incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

The novel features of the invention are set forth with particularity inthe appended claims. A better understanding of the features andadvantages of the present invention will be obtained by reference to thefollowing detailed description that sets forth illustrative embodiments,in which the principles of the invention are utilized, and theaccompanying drawings of which:

FIG. 1 shows a schematic of a tooth in a current position, a desiredtarget position, an actual resulting position from the application of aplain polymeric shell appliance, an overcorrected position, and anactual resulting position from the application of a polymeric shellappliance of the present disclosure, according to many embodiments;

FIG. 2 shows a flowchart of a method of manufacturing a set of polymericshell appliances with overcorrection, according to many embodiments;

FIG. 3 shows a graph of the discrepancy between a planned tooth path andan overcorrected tooth path, according to many embodiments;

FIG. 4 shows a schematic of a tooth in a current position, a nextplanned position, and an overcorrected position, according to manyembodiments;

FIG. 5 shows a flowchart of a method of manufacturing a set of polymericshell appliances with overcorrection, according to many embodiments;

FIG. 6 shows a schematic of rotational tooth movement generated by apolymeric shell appliance, according to many embodiments; and

FIG. 7 shows a flowchart of a method of manufacturing a set of polymericshell appliances with overcorrection, according to many embodiments.

DETAILED DESCRIPTION

The present disclosure provides systems and methods to generatemodified, overcorrected positions for a set of appliances such aspolymeric shell appliances.

In one aspect, a system for moving one or more teeth with a dentalappliance is provided. The system comprises a database comprising datacorresponding to one or more of: (1) a plurality of discrepanciesbetween target positions of teeth and achieved positions of the teeth inresponse to treatment, (2) a plurality of correlations between teethmovements and force systems applied by dental appliances, or (3) aplurality of clinical results of achieved teeth movements in response toforce systems applied by dental appliances. The system can comprise aprocessing unit coupled to the database, wherein the processing unit isconfigured to determine an initial position of each of the one or moreteeth, determine a target position for each of the one or more teeth ina treatment plan, and determine a movement vector to move said each ofthe one or more teeth from the initial position to the target positionwith an overcorrected tooth receiving cavity position determined inresponse to the data in the database.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the data corresponds to the plurality ofdiscrepancies, the plurality of discrepancies comprising a discrepancyof one or more of a force system, an achievement matrix, or clinicalknowledge.

In many embodiments, the processing unit is configured to modify one ormore tooth receiving cavity geometries of the dental appliance based onthe overcorrected position.

In many embodiments, the movement vector is configured to establish aforce system applied by the dental appliance to each tooth to move thetooth from the initial position to the target position with theovercorrected tooth receiving cavity position. The force system, whenapplied by the dental appliance, can move the tooth from the initialposition to a position closer to the target position than theovercorrected tooth receiving cavity position. The force system cancomprise one or more of a force, a moment of a force, or a moment of acouple.

In many embodiments, the movement vector is further determined inresponse to one or more of a minimum or maximum vertex distance.

In many embodiments, the processing unit is further configured todetermine an overcorrected tooth receiving cavity corresponding to theovercorrected tooth receiving cavity position, the overcorrected toothreceiving cavity comprising a three dimensional shape profile to receivea corresponding tooth having a corresponding three dimensional shapeprofile, the three dimensional shape profile of the tooth receivingcavity being one or more of rotated or translated relative to thecorresponding three dimensional shape profile of the corresponding toothin the target position in order to define the overcorrected toothreceiving cavity position.

In many embodiments, the dental appliance comprises a polymeric shellappliance.

In many embodiments, the processing unit is further configured togenerate instructions for fabricating a dental appliance in accordancewith any of the embodiments herein, wherein the dental appliancecomprises a tooth receiving cavity having the overcorrected toothreceiving cavity position. The dental appliance, when positioned on theone or more teeth, can be shaped to move the one or more teeth from theinitial position toward the target position along the movement vector.

In another aspect, a method for determining one or more tooth receivingcavity positions of a dental appliance for moving one or more teeth isprovided. The method can comprise: providing a database comprising datacorresponding to one or more of: (1) a plurality of discrepanciesbetween target positions of teeth and achieved positions of teeth inresponse to treatments, (2) a plurality of correlations between teethmovements and force systems applied by dental appliances, or (3) aplurality of clinical results of achieved teeth movements in response toforce systems applied by dental appliances; determining an initialposition of the one or more teeth; determining a target position of eachof the one or more teeth in a treatment plan; and determining anovercorrected position of one or more tooth receiving cavities of thedental appliance in response to the data in the database.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the data corresponds to the plurality ofdiscrepancies, the plurality of discrepancies comprising a discrepancyof one or more of a force system, an achievement matrix, or clinicalknowledge.

In many embodiments, the method further comprises modifying a geometryof the one or more tooth receiving cavities of the dental appliancebased on the overcorrected position.

In many embodiments, the dental appliance is configured to apply a forcesystem to the tooth to move the tooth from the initial position to thetarget position with the overcorrected tooth receiving cavity position.The force system, when applied by the dental appliance, can move thetooth from the initial position to a position closer to the targetposition than the overcorrected position. The force system can compriseone or more of a force, a moment of a force, or a moment of a couple.

In many embodiments, determining the overcorrected position compriseslimiting the overcorrected position in response to one or more of aminimum or maximum vertex distance.

In many embodiments, the method further comprises determining anovercorrected tooth receiving cavity corresponding to the overcorrectedtooth receiving cavity position, the overcorrected tooth receivingcavity comprising a three dimensional shape profile to receive acorresponding tooth having a corresponding three dimensional shapeprofile, the three dimensional shape profile of the tooth receivingcavity being one or more of rotated or translated relative to thecorresponding three dimensional shape profile of the corresponding toothin the target position in order to define the overcorrected position.

In many embodiments, the dental appliance comprises a polymeric shellappliance.

In many embodiments, the method further comprises generatinginstructions for fabricating a dental appliance in accordance with anyof the embodiments herein, wherein the dental appliance comprises atooth receiving cavity having the overcorrected tooth receiving cavityposition. The dental appliance, when positioned on the one or moreteeth, can be shaped to move the one or more teeth from the initialposition toward the target position along the movement vector. Themethod can further comprise fabricating the dental appliance.

In another aspect, a system for moving one or more teeth with a dentalappliance is provided. The system can comprise a database comprisingdata corresponding to a plurality of discrepancies between targetpositions of teeth and achieved positions of the teeth in response totreatment, and a processing unit coupled to the database. The processingunit can be configured to determine one or more initial positions of theone or more teeth, determine a target position for each of the one ormore teeth in a treatment plan, and determine a movement vector to movesaid each of the one or more teeth from the initial position to thetarget position with an overcorrected tooth receiving cavity positiondetermined in response to the plurality of discrepancies.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the plurality of discrepancies comprises adiscrepancy of one or more of a force system, an achievement matrix, orclinical knowledge.

In many embodiments, the processing unit is configured to modify one ormore tooth receiving cavity geometries of the dental appliance based onthe overcorrected position.

In many embodiments, the movement vector is configured to establish aforce system applied by the dental appliance to the tooth to move thetooth from the initial position to the target position with theovercorrected tooth receiving cavity position. The force system, whenapplied by the dental appliance, may move the tooth from the initialposition to a position closer to the target position than theovercorrected tooth receiving cavity position. The force system cancomprise one or more of a force, a moment of a force, or a moment of acouple.

In many embodiments, the movement vector is further determined inresponse to one or more of a minimum or maximum vertex distance.

In many embodiments, the processing unit is configured to receive asinput initial positions of each of the one or more teeth and finalpositions of each of the one or more teeth, to determine a plurality ofstages corresponding to a plurality of appliances to move the one ormore teeth from the initial positions to the final positions, todetermine the target position along a movement path of each of the oneor more teeth for each stage and to determine the overcorrected positionof each of the one or more teeth in response to the target positionalong the movement path for each stage.

In another aspect, a system for moving one or more teeth with a dentalappliance is provided. The system can comprise a database comprising aplurality of correlations between teeth movements and force systemsapplied by dental appliances, and a processing unit coupled to thedatabase. The processing unit can be configured to determine an initialposition of the one or more teeth, determine a target position for eachof the one or more teeth in a treatment plan, and determine a movementvector to move said each of the one or more teeth from the initialposition to the target position with an overcorrected tooth receivingcavity position different from the target position in response to theplurality of correlations.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the processing unit is configured to modify one ormore tooth receiving cavity geometries of the dental appliance based onthe overcorrected position.

In many embodiments, the movement vector is configured to establish aforce system applied by the dental appliance to the tooth to move thetooth from the initial position to the overcorrected position. The forcesystem, when applied by the dental appliance, may move the tooth fromthe initial position to a position closer to the target position thanthe overcorrected position. The force system can comprise one or more ofa force, a moment of a force, or a moment of a couple.

In many embodiments, the movement vector is further determined inresponse to one or more of a minimum or maximum vertex distance.

In many embodiments, the processing unit is configured to receive asinput initial positions of each of the one or more teeth and finalpositions of each of the one or more teeth, to determine a plurality ofstages corresponding to a plurality of appliances to move the one ormore teeth from the initial positions to the final positions, todetermine the target position along a movement path of each of the oneor more teeth for each stage and to determine the overcorrected positionof each of the one or more teeth in response to the target positionalong the movement path for each stage.

In another aspect, a system for moving one or more teeth with a dentalappliance is provided. The system can comprise a database comprising aplurality of clinical results of achieved teeth movements in response toforce systems applied by dental appliances, and a processing unitcoupled to the database. The processing unit can be configured todetermine an initial position of the one or more teeth, determine atarget position for each of the one or more teeth in a treatment plan,and determine a movement vector to move said each of the one or moreteeth from the initial position to the target position with anovercorrected tooth receiving cavity position determined in response tothe plurality of clinical results.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the processing unit is configured to modify a toothreceiving cavity geometry of the dental appliance based on theovercorrected position.

In many embodiments, the movement vector is configured to establish aforce system applied by the dental appliance to the tooth to move thetooth from the initial position to the overcorrected position. The forcesystem, when applied by the dental appliance, may move the tooth fromthe initial position to a position closer to the target position thanthe overcorrected position. The force system can comprise one or more ofa force, a moment of a force, or a moment of a couple.

In many embodiments, the movement vector is further determined inresponse to one or more of a minimum or a maximum vertex distance.

In many embodiments, the processing unit is configured to receive asinput initial positions of each of the one or more teeth and finalpositions of each of the one or more teeth, to determine a plurality ofstages corresponding to a plurality of appliances to move the one ormore teeth from the initial positions to the final positions, todetermine the target position along a movement path of each of the oneor more teeth for each stage and to determine the overcorrected positionof each of the one or more teeth in response to the target positionalong the movement path for each stage.

In another aspect, a method for determining one or more tooth receivingcavity positions of a dental appliance for moving one or more teeth isprovided. The method can comprise: providing a database comprising priortreatment data corresponding to a plurality of discrepancies betweentarget positions of teeth and achieved positions of teeth in response totreatments; determining an initial position of the one or more teeth;determining a target position of each of the one or more teeth in atreatment plan; and determining an overcorrected position of the one ormore tooth receiving cavities in response the prior treatment data.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the dental appliance is configured to apply a forcesystem to the tooth to move the tooth from the initial position to theovercorrected position. The force system, when applied by the dentalappliance, can move the tooth from the initial position to a positioncloser to the target position than the overcorrected position. The forcesystem can comprise one or more of a force, a moment of a force, or amoment of a couple.

In many embodiments, determining the overcorrected position compriseslimiting the overcorrected position in response to one or more of aminimum or maximum vertex distance.

In another aspect, a method for moving one or more teeth with a dentalappliance is provided. The method can comprise providing a databasecomprising a plurality of correlations between teeth movements and forcesystems applied by dental appliances; and determining one or moreovercorrected positions of one or more tooth receiving cavities of thedental appliance in response to the plurality of correlations.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the dental appliance is configured to apply a forcesystem to the tooth to move the tooth from the initial position to theovercorrected position. The force system, when applied by the dentalappliance, can move the tooth from the initial position to a positioncloser to the target position than the overcorrected position. The forcesystem can comprise one or more of a force, a moment of a force, or amoment of a couple.

In many embodiments, determining the overcorrected position compriseslimiting the overcorrected position in response to one or more of aminimum or maximum vertex distance.

In another aspect, a method for determining positions of one or moretooth receiving cavities of a dental appliance for moving one or moreteeth is provided. The method can comprise providing a databasecomprising a plurality of clinical results of achieved teeth movementsin response to force systems applied by dental appliances; anddetermining an overcorrected position of the one or more tooth receivingcavities in response to the plurality of clinical results of achievedteeth movements in response to force systems applied by dentalappliances.

In many embodiments, the database comprises one or more of patienttreatment histories, orthodontic therapies, orthodontic information, ordiagnostics.

In many embodiments, the dental appliance is configured to apply a forcesystem to the tooth to move the tooth from the initial position to theovercorrected position. The force system, when applied by the dentalappliance, can move the tooth from the initial position to a positioncloser to the target position than the overcorrected position. The forcesystem can comprise one or more of a force, a moment of a force, and amoment of a couple.

In many embodiments, determining the overcorrected position compriseslimiting the overcorrected position in response to one or more of aminimum or maximum vertex distance.

In another aspect, a method for moving teeth of a patient is provided.The method can comprise: providing a first appliance having a firstplurality of overcorrected tooth-receiving cavities to move the teeth tofirst target positions, the first overcorrected tooth receiving cavitieshaving positions different from the first target positions by firstamounts; and providing a second appliance having a second plurality ofovercorrected tooth-receiving cavities to move the teeth to secondtarget positions, the second overcorrected tooth receiving cavitieshaving positions different from the second target positions by secondamounts; wherein the second amounts are less than the first amounts.

In many embodiments, the first amounts comprise a first plurality offirst amounts and the second amounts comprise a second plurality ofsecond amounts, each of the second plurality of second amounts less thana corresponding first amount of the first plurality of first amounts.

In many embodiments, the second overcorrections are provided after thefirst overcorrections. Alternatively, the second overcorrections can beprovided before the first overcorrections.

In many embodiments, the method further comprises providing a thirdappliance having a third plurality of overcorrected tooth-receivingcavities to move the teeth to third target positions, the thirdovercorrected tooth receiving cavities having positions different fromthe third target positions by third amounts, wherein the third amountsare less than the first and second amounts. The third appliance can beprovided before or after the second appliance.

In another aspect, a system for moving teeth of a patient is provided.The system can comprise: a first appliance having a first plurality ofovercorrected tooth-receiving cavities to move the teeth to first targetpositions, the first overcorrected tooth receiving cavities havingpositions different from the first target positions by first amounts;and a second appliance having a second plurality of overcorrectedtooth-receiving cavities to move the teeth to second target positions,the second overcorrected tooth receiving cavities having positionsdifferent from the second target positions by second amounts; whereinthe second amounts are less than the first amounts.

In many embodiments, the first amounts comprise a first plurality offirst amounts and the second amounts comprise a second plurality ofsecond amounts, each of the second plurality of second amounts less thana corresponding first amount of the first plurality.

In many embodiments, the system further comprises a third appliancehaving a third plurality of overcorrected tooth-receiving cavities tomove the teeth to third target positions, the third overcorrected toothreceiving cavities having positions different from the third targetpositions by third amounts, wherein the third amounts are less than thefirst and second amounts.

In another aspect, for a system or a method according to any of theembodiments herein, the one or more teeth comprise a plurality of teeth,and the appliance comprises a plurality of overcorrected teeth receivingcavities.

In another aspect, for a system or a method according to any of theembodiments herein, each overcorrected tooth receiving cavity comprisesa three dimensional shape profile to receive a corresponding toothhaving a corresponding three dimensional shape profile, the threedimensional shape profile of the tooth receiving cavity one or more ofrotated or translated relative to the corresponding three dimensionalshape profile of the corresponding tooth in the target position in orderto define the overcorrected tooth receiving cavity position.

In another aspect, for a system or a method according to any of theembodiments herein, the overcorrected tooth receiving cavity comprisesan over correction of a three-dimensional shape profile along one ormore of six degrees of freedom of the tooth receiving cavity of saideach of the one or more teeth.

In another aspect, for a system or a method according to any of theembodiments herein, the appliance comprises a polymeric shell applianceand the polymeric shell appliance has been directly manufactured withone or more of 3D printing, stereo lithography, or fused depositionmodeling.

In another aspect, a method for moving one or more teeth is providedcomprising providing a system according to any of the embodimentsherein.

In another aspect, a system or a method according to any of theembodiments herein further comprises instructions for manufacturing thedental appliance.

The methods, systems, and apparatus disclosed herein can be combined inmany ways and may comprise one or more components of known polymer shellappliances. Known shell appliances to reposition teeth may includefeatures to facilitate the predictability of teeth movement. Forexample, such features may include “Active Attachment,” “Activator,”“Pressure Point,” “Bite ramp,” and “Power ridge” available in productsof Align Technology, Inc. of Santa Clara, Calif. Such features maydepend on adding features to the plain shell appliance and/or the teeth.For example, by active attachment with an activator or attachment, moretorque can be created to rotate the canine or premolar. The power ridgemay be used to create torque to move root in buccal-lingual direction.The polymer shell appliance inner surface may then be modified partiallynear the features attached or added to a tooth. However, the majority ofthe surface of the polymeric shell appliance may still be in theoriginal position (i.e., the intended position of the teeth for theparticular stage of treatment) and unchanged. The instant applicationrefers to such a polymeric shell appliance as a “plain polymeric shellappliance.”

As used herein, the terms “target position” and “planned position” areused interchangeably.

As used herein, the terms “patient” and “subject” are usedinterchangeably.

Although reference is made to an appliance comprising a polymeric shellappliance, the embodiments disclosed herein are well suited for use withmany appliances that receive teeth, for example appliances without oneor more of polymers or shells. The appliance can be fabricated with oneor more of many materials such as metal, glass, reinforced fibers,carbon fiber, composites, reinforced composites, aluminum, biologicalmaterials, and combinations thereof for example. The appliance can beshaped in many ways, such as with thermoforming or direct fabrication asdescribed herein, for example. Alternatively or in combination, theappliance can be fabricated with machining such as an appliancefabricated from a block of material with computer numeric controlmachining.

Examples of appliances such as polymeric shell appliances suitable forincorporation in accordance with embodiments of the present disclosuresuitable are described in U.S. application Ser. No. 12/623,340, filed onNov. 20, 2009, published as US 2010/0138025 on Jun. 3, 2010, entitled“Orthodontic systems and methods including parametric attachments”, andU.S. application Ser. No. 13/865,091, filed on Apr. 17, 2013, publishedas US 2013/0230818, entitled “Method and system for optimizing dentalaligner geometry”, the entire disclosures of which are incorporatedherein by reference.

In many instances and for many movements, a plain polymeric shellappliance may work well. Features can be added when there are difficultmovements such as significant rotation, extrusion, or root movement.Even so, the plain polymeric shell appliance itself can still create themajority of force and moment to move the tooth.

A manufacturing process for a plain polymeric shell appliance may be asfollows. First, initial and final teeth positions may be acquired, and amovement path may be generated of all the teeth. Then, additionalfeatures such as attachments, dimples, and ridges may be added to theteeth. A 3D printer may then be used to print the physical mold of theteeth, jaw, and other features. A thin plastic sheet may be thermalformed on the mold. The gingival line may be cut, and the polymericshell appliance may be removed from the mold. Finally, the plainpolymeric shell appliance may be cleaned and packaged.

In many embodiments, a processor comprises a user input and display fora user to position and orient a plurality of teeth at target positionsand orientations for each stage of a treatment. Alternatively, the usermay input position and orient the plurality of teeth at target finalpositions and orientations for the final stage of a treatment, and theprocessor may determine positions and orientations of the teeth at eachof a plurality of intermediate stages of treatment. The processor mayreceive as input the plurality of initial positions and initialorientations of the teeth. The processor may comprise instructions toposition teeth receiving cavities of the appliance at positions awayfrom the target positions and orientations for each stage of a pluralityof stages of the treatment in order to provide activation energy to theappliance. The processor may comprise instructions to output thepositions of the teeth receiving cavities away from the target positionsand orientations for each stage of the plurality of stages. Theprocessor may comprise instructions to manufacture a plurality ofappliances with indirect manufacturing comprising thermoforming ordirect manufacturing comprising one or more of 3D printing,stereolithography, or fused deposition modeling, for example. In manyembodiments, the processor generates instructions for fabricating one ormore appliances and transmits the instructions to a fabrication machine,e.g., configured to fabricate the appliances using indirectmanufacturing or direct manufacturing, or combinations thereof.

The plain polymeric shell appliance can be made from the tooth positionfrom the initial and final positions. In software, for example, thetooth position can be designed with the following principles in mind.The teeth may not collide with each other in all stages, or else thecourse of treatment can include removal of parts of one or more teeth.Additionally, in some embodiments, teeth are not moved too fast becauseof biological limitations.

Accordingly, the tooth movement path generated for each stage oftreatment can be related to the limit that the tooth can be moved forthe particular stage of treatment. The polymeric shell appliance itself,however, can be used to move the tooth but not to limit tooth movement,for example. The force from a polymeric shell appliance can be createdbecause the appliance can be based on the teeth positioning of the nextstage of treatment and put on the full dentition of the patient in thecurrent stage of treatment.

In this present disclosure, improved methods of creating polymeric shellappliances are provided. Instead of creating a polymeric shell appliancewith teeth receiving cavities corresponding to the position of a toothin the next stage of treatment, the appliance can be created based on amodified, overcorrected tooth position, for example. In this modifiedtooth position, force and moment may be created to move the tooth rootin the desired direction, rather than limiting the tooth to nextposition. A schematic of a modified tooth position for targeting thetooth root is shown in FIG. 1.

FIG. 1 shows a schematic of a tooth in various positions—a currentposition 102 (e.g., current position 102 a), a desired target position104 comprising the planned location of the tooth at the end of thetreatment stage (e.g., next planned position 104 a), an actual resultingposition 106 from the application of a plain polymeric shell appliance(e.g., an achieved position with no overcorrection 106 a, which mayexhibit lag in the translation and/or tipping relative to the nextplanned position 104 a), an overcorrected position 112 (e.g.,overcorrected position 112 a, which may exhibit more translation tocreate more force and/or rotation to compensate for tipping and to movethe root relative to the next planned position 104 a), and an actualresulting position 114 from the application of a polymeric shellappliance of the present disclosure configured to overcorrect asdescribed herein (e.g., achieved position with overcorrection 114 a,which may be close to or substantially match the next planned position104 a). Because the force and moment generated can decrease as theappliance and tooth discrepancy decreases, there can be a discrepancybetween the desired target position 104 and the actual position 106 thatis achieved. There may be a lag in the translation of the tooth asindicated by the arrow 108. There may be tipping or rotation from theroot as indicated by the arrow 110. According to embodiments of thepresent disclosure, a polymeric shell appliance may be configured withthe tooth receiving cavities of the appliance at locations correspondingto an overcorrected position 112. More translation may be providedversus the uncorrected appliance to create more force. Rotation may beadded to compensate for the tipping effect and move the root. The forceand moment generated can decrease as the discrepancy between applianceand tooth decreases. A discrepancy can remain, however, between theovercorrected position 112 of the tooth receiving cavity and the actualposition 114 that is achieved, as the tooth moves toward the targetposition. The resulting position 114 from the overcorrection can moreclosely match the desired target position 104 in the course oftreatment.

The appliances such as polymeric shell appliances can be configured inone or more of many ways with the overcorrected tooth receiving cavitiesto move one or more teeth as described herein. The tooth comprises atooth profile, such as a three-dimensional shape profile, and the toothreceiving cavity of the polymeric shell appliance may comprise acorresponding internal three dimensional shape profile to receive thetooth. The position of the shape profile of the tooth receiving cavityof the polymeric shell appliance can be overcorrected in relation to thenext planned position of the tooth. Alternatively or in combination, theorientation of the three dimensional shape profile of the toothreceiving cavity can be overcorrected in relation to the next plannedorientation of the tooth.

The overcorrection with the three-dimensional shape profile of the toothreceiving cavity can be provided along one or more of six degrees offreedom. The overcorrection can be provided along two or more degrees offreedom, for example along one translational and one rotational degreeof freedom. The overcorrection can be provided along three or moredegrees of freedom, for example along two translational and onerotational degree of freedom. The amount of overcorrection along eachdegree of freedom can be determined in response to clinical data, forexample. Additional degrees of freedom of the tooth receiving cavitiescan be overcorrected to move the tooth to the planned position andorientation.

The appliance can be configured to move a plurality of teeth with aplurality of overcorrected tooth receiving cavities at each of aplurality of stages of the treatment as described herein. Each of theplurality of overcorrected tooth receiving cavities can be configured tomove the corresponding tooth of the plurality of teeth to the plannedtarget position.

Referring to FIG. 2, an exemplary method 200 of creating a polymericshell appliance may be as follows. In a step 202, the initial positionof the teeth of a subject may be acquired and input to a processor. In astep 204, the final, desired position of the teeth of the subject at theend of a course of treatment may be determined and input to a processor.In a step 206, the movement path for each tooth may be designed. Themovement path may be designed such that, at each stage of treatment, theteeth may not collide with each other and may move at a limited speed(e.g., 0.25 mm/treatment stage, which may for example be 2 weeks). In astep 208, the tooth movement from the current stage to next stage ornext several stages may be acquired. In a step 210, the tooth positionof next stage may be modified so sufficient force is created (i.e., thediscrepancy from the current to next stage is sufficiently large) tomove the tooth closely to the desired target position. The modificationof step 210 can be performed with an overcorrection in one or more ofmany ways. For example, the tooth position may be overcorrected asdescribed herein. In a step 212, more root movement may be added tocompensate for the tooth root lagging during the movement, for examplewith overcorrection of one or more of the position or orientation of thetooth receiving cavity. In a step 214, rotation may be added tocompensate and overcome the tipping effect while tooth is in bodilytranslation (e.g., for space closure treatment), for example withovercorrection of one or more of the position or orientation of thetooth receiving cavity. In a step 216, other changes may be applied toimprove the force or moment applied, for example with overcorrection ofone or more of the position or orientation of the tooth receivingcavity. In a step 218, a mold of all teeth in the modified aligner(i.e., overcorrected polymeric shell appliance) tooth position and jawmay be created. Other features such as like attachment and power ridgesmay be added. The mold may be created using 3D printing technology, forexample. In a step 220, a thin plastic sheet may be thermal formed tothe mold to create the aligner or appliance. In a step 222, the gingivalline may be cut from the molded sheet and the aligner or appliance maybe removed from the mold. In a step 224, the aligner or appliance may becleaned and packaged. Alternatively or in combination, the appliance canbe fabricated directly, for example with one or more of 3D printing,stereo lithography, or fused deposition modeling of the appliance, forexample.

Although the above steps show the method 200 of generating a set ofpolymeric shell appliances overcorrected to move teeth in an improvedmanner in accordance with many embodiments, a person of ordinary skillin the art will recognize many variations based on the teachingdescribed herein. The steps may be completed in a different order. Stepsmay be added or deleted. Some of the steps may comprise sub-steps. Manyof the steps may be repeated as often as beneficial to the treatment.

One or more of the steps of the method 200 may be performed withcircuitry as described herein, for example one or more of a processor orlogic circuitry of a computer or a computerized system. The circuitrymay be programmed to provide one or more of the steps of the method 200,and the program may comprise program instructions stored on a computerreadable memory or programmed steps of the logic circuitry, for example.

Aspects of the present disclosure provide several ways to modify thetooth position for the aligner or polymeric shell appliances, which arediscussed herein and as follows. The methods of modifying the toothposition may be applied alone, in various combinations, or in variouscombinations of their component steps or parts.

1. Modify Tooth Position Based on Achievement Statistics

The appropriate overcorrection may be determined using achievementstatistics. Achievement statistics describe the relationship between theachieved and planned tooth movement for post treatment (or in the middletreatment) cases. A tooth can be considered as a rigid body and itsmovement can be described by 6 degrees of freedom (DOFs), or 3translation and 3 rotations. Optionally, the achievement statisticsprovide data corresponding to discrepancies between achieved and plannedtarget positions of teeth in response to treatment.

After the treatment, the teeth are moved to a new position close to theplanned final position, but not exactly the same. The movement from theinitial tooth position to this new position may be called the achievedmovement. The achieved movement can be measured by taking a newimpression and comparing it to the initial impression. Alternatively orin combination, other types of data besides impressions can be used,such as scans or images of the teeth.

The relationship between the planned movement and the achieved movementcan be described by a statistical relationship called aPlanned-Achievement Relation.

The achievement statistics can show coupling among planned movements andachieved movements, and cross-coupling among terms can be used to designthe polymeric shell appliance.

The Planned-Achievement Relation can be estimated by data analysis of alarge number of treated cases. In some embodiments, linear regressionmay be used.

The Planned-Achievement Relation estimated from the after treatmentcases can represent full movement, i.e., from an initial position of theteeth to the final position of the teeth. The Planned-AchievementRelation for a single stage (which may be referred to as a stagePlanned-Achievement Relation) can be computed from the fullPlanned-Achievement Relation when the stage number is known. Theovercorrection can be computed from the Planned-Achievement Relation.From the Planned-Achievement Relation, it can be known that the desiredfinal positions of the teeth may not be fully achieved using a plainaligner or polymeric shell appliance. An overcorrection may be used toamplify and correct the movement.

However, the overcorrection movement can be adjusted more to deal withcomplicated tooth movement. A consideration may be to blend theovercorrection with planned movement. In some embodiments, whentreatment is started, the overcorrection should not be too great becausea greater than necessary overcorrection may apply too great a force tothe root and cause the patient pain and/or discomfort. After severalweeks, teeth may start moving and the bone near the root may get softbecause of the biological response. Then, further overcorrection can beadded. In some embodiments, when the treatment is reaching the finalstage, the overcorrection can be reduced to let the tooth move closer tothe final position, rather than having a larger overcorrection position.

The data from clinical studies can be fit, for example, with a linearregression of the coefficients of the achievement matrix and R2 valuesdetermined.

The change of overcorrection is shown in the overcorrection graph 400 ofFIG. 3. The graph 400 shows the planned tooth path 402 of one or moreteeth of the subject, and the overcorrected tooth receiving cavity path404 for a plurality of stages of treatment, e.g., 0 (initial prior totreatment), 1, 2, etc. to N, where N is the final stage. The graph 400includes a line for the planned tooth path 402, which can be compared tothe overcorrected tooth path 404. There may be greater overcorrection atearly stage 406 versus at the later stage 408. Each stage has a plannedtooth position of the subject and a corresponding overcorrected toothposition of the tooth receiving cavity of the appliance as shown withthe dashed line of stages 1 and 2, for example. Each of the plurality ofteeth receiving cavities of an appliance for a stage can beovercorrected with reference to the tooth position as described herein.The tooth receiving cavities of the final stage may or may not beovercorrected, and the appliance may be left on the teeth for a longeramount of time to ensure that the teeth have moved to the final targetpositions.

The processing unit as described herein can be configured withinstructions to receive as input initial positions of each of the one ormore teeth and final positions of each of the one or more teeth. Theprocessing unit can be configured with instructions to determine aplurality of stages corresponding to a plurality of appliances to movethe one or more teeth from the initial positions to the final positions.The processing unit can be configured to determine the target positionalong a planned movement path of each of the one or more teeth for eachstage and to determine the overcorrected position of each of the one ormore tooth receiving cavities in response to the target position alongthe movement path for each stage, for example.

The overcorrection may be gradually reduced to none as the treatmentcourse nears completion. Such reduction in the overcorrection may beprovided to allow the soft tissue of the patient to begin to set, forexample.

Improved methods and systems to move teeth by applying such graduallydecreasing overcorrections are provided by the present disclosure. Thepositions of the tooth receiving cavities of the appliance can belocated to provide overcorrection force vectors to the teeth. Forexample, if the target location of the tooth for the present stage islocated 0.2 mm from the position of the immediately prior stage, thetooth receiving cavity can be located 0.3 mm from the position of theprior stage in order to provide overcorrection with the desired forcevector, for example. A first overcorrected force vector may be appliedon teeth to move the teeth to a first target position with a firstovercorrected tooth receiving cavity of a first appliance. The firstovercorrected force vector may have a first overcorrection directed tomove the teeth to a first overcorrected position different from thefirst target position. A second overcorrected force vector may then beapplied on the teeth to move the teeth to a second target position witha second overcorrected tooth receiving cavity of a second appliance. Thesecond overcorrected force vector may have a second overcorrectiondirected to move the teeth to a second overcorrected position differentfrom the second target position. The second overcorrection may be lessthan the first overcorrection and may be applied after the firstovercorrection. A third overcorrected force vector may be applied on theteeth to move the teeth to a third target position with a third overcorrected tooth receiving cavity of a third appliance. The thirdovercorrected force vector may have a third overcorrection directed tomove the teeth to a third overcorrected position different from thethird target position. The third overcorrection may be less than thefirst and second overcorrections. First, second, and/or third shellappliances having first, second, and/or third pluralities oftooth-receiving cavities, for example, may be provided and configured toapply the first, second, and/or third overcorrected force vectors on thetooth, for example. A person of ordinary skill in the art will recognizevariations in one or more of the order, timing or amount ofovercorrection.

Another adjustment may include the minimum and maximum crown movement.In some embodiments, to move the tooth, enough force but not too largeof a force should be applied to the tooth. For an aligner or polymericshell appliance, the force created can be related to the discrepancybetween the aligner or appliance to the tooth. The overcorrectionmovement can be modified as follows and as described herein.

The maximum movement distance for all crown surface points, from thecurrent position to the overcorrection position, can be measured. Thismaximum vertex distance can be bigger than one number, for example, 0.2mm. This distance can be less than another number, for example 0.50 mm.If the distance is too big or small, the overcorrection movement can beincreased or reduced by multiplying the movement vector.

FIG. 4 shows a schematic of tooth positions and is an example of a toothin a current position 502, a planned target position 504, and anovercorrected target position 506. It can be seen that the overcorrectedtarget position 506 can involve more movement than the planned targetposition 504, particularly for root part 508. The greater movement maybe because the root can be normally hard to move so the aligner orpolymeric shell appliance can be manufactured to move root 508 more.

FIG. 5 shows a flow chart of a method 600 of creating a polymeric shellappliance using an “achievement matrix” as described herein and above.In a step 602, after treatment cases for various patients may becollected. In a step 604, impressions of the dentition of the variouspatients may be made before and after the treatment to estimate thetooth movement achieved. In a step 606, the impressions may be matchedto estimate the achieved tooth movement. Alternatively or incombination, other types of data besides impressions can be used, suchas scans or images of the dentition before and after treatment. In astep 608, an achievement matrix may be built using the estimatedachieved tooth movements of the various embodiments. The achievementmatrix may be built using data analysis such as linear regression. In astep 610, the achievement matrix may be inverted to generate theovercorrection matrix. The achievement matrix can be used to correcttooth movement in response to one or more discrepancies. In a step 612,the overcorrection movement for each treatment stage may be generated byacquiring the plan movement vector for each treatment stage andmultiplying by the overcorrection matrix. In a step 614, theovercorrection movement may be adjusted so the maximum vertex movementof the crown is not too small or too large (e.g., greater than 0.2 mmand less than 0.5 mm). In a step 616, the overcorrection movement may beapplied to the current treatment stage to obtain the modified toothposition. In a step 618, an aligner or polymeric shell appliance may becreated from the modified tooth positions of all teeth.

Although the above steps show the method 600 of generating a set ofpolymeric shell appliances overcorrected to move teeth in an improvedmanner in accordance with many embodiments, a person of ordinary skillin the art will recognize many variations based on the teachingdescribed herein. The steps may be completed in a different order. Stepsmay be added or deleted. Some of the steps may comprise sub-steps. Manyof the steps may be repeated as often as beneficial to the treatment.

One or more of the steps of the method 600 may be performed withcircuitry as described herein, for example one or more of a processor orlogic circuitry of a computer or a computerized system. The circuitrymay be programmed to provide one or more of the steps of the method 600,and the program may comprise program instructions stored on a computerreadable memory or programmed steps of the logic circuitry, for example.

2. Modify Tooth Position Based on Clinical and/or Mechanical Knowledge.

Another method of generating the overcorrections may be to use clinicaland/or mechanical knowledge based on a history of multiple cases oftreatment to move teeth with aligners or polymeric shell appliances. Theclinical and/or mechanical knowledge can provide information regardingcorrelations between teeth movements and force systems applied by dentalappliances, as well as clinical results of achieved teeth movements inresponse to force systems applied by dental appliances.

For example, when using aligners or polymeric shell appliances to treata premolar extraction case, there may be an undesirable tipping effectof the canine when the space is closed. When the canine is translateddistally, force can be mostly applied to the crown, which can tip thecanine toward the molar. After the treatment is finished, the canineroot may be straight and not aligned well with the other teeth. Tobetter straighten and align the canine root, an attachment may beprovided to the canine to add more torque and compensate for thetipping. Alternatively or in combination, the tooth position may bemodified with some rotation or torque.

Referring to FIG. 6, to create such a modified position, one may firstdetermine whether premolar extraction or space closure treatment isappropriate. For canines 1002, the root apex may be rotated distally(around the X axis of the crown basis) as indicated by the arrow 1004and lingually (around the Y axis of the crown basis) as indicated by thearrow 1006. The tipping from the distal translation as indicated byarrow 1008 and lingual movement as indicated by arrow 1010 can therebybe compensated. For the activation of a second premolar 1012, the rootapex can be rotated mesially (around the X axis of the crown basis) asindicated by the arrow 1014 and the second premolar can be translateddistally as indicated by the arrow 1016 in the meantime.

Referring to FIG. 7, a method 1100 of generating an overcorrectedpolymeric shell appliance can be as follows. First, the initial andfinal positions of teeth in the course of treatment may be determined ina step 1102. Then, the tooth movement path may be defined based onclinical limitations in a step 1104, for example, to avoid the toothcollision and velocity (0.25 mm/2 weeks). From the first tooth movementpath, a second tooth movement path may be created in a step 1106 andused to generate an aligner or polymeric shell appliance in a step 1108.The limitation(s) of the tooth arrangement in the second path can bebigger than that of the first path. For example, tooth collision may beallowed, and the velocity can be bigger than 0.25 mm for 2 weeks.

The knowledge to generate the second tooth movement path or arrangementcan be drawn from various sources. In a step 1110, for example, dataanalysis may be performed for past treatment cases. In a step 1112, forexample, the mechanical properties (i.e., the force/torque created) ofvarious aligners or polymeric shell appliances may be measured in alaboratory. In a step 1114, for example, the overcorrection may accountfor attachments to the teeth such as a power ridge and the like. If anattachment is used, the overcorrection can be small because attachmentmay already help engagement and create force. In a step 1116, forexample, previous clinical knowledge may be applied. In a step 1118, theovercorrection or modification from the first to second tooth paths maybe larger for the initial and middle stages of the treatment, whilegetting smaller when the treatment is close to completed so that thefinal tooth arrangement is close to the final position.

In a step 1120, an overcorrected appliance is generated in response toone or more discrepancies as described above.

Although the above steps show the method 1100 of generating a set ofpolymeric shell appliances overcorrected to move teeth in an improvedmanner in accordance with many embodiments, a person of ordinary skillin the art will recognize many variations based on the teachingdescribed herein. The steps may be completed in a different order. Stepsmay be added or deleted. Some of the steps may comprise sub-steps. Manyof the steps may be repeated as often as beneficial to the treatment.

One or more of the steps of the method 1100 may be performed withcircuitry as described herein, for example one or more of a processor orlogic circuitry of a computer or a computerized system. The circuitrymay be programmed to provide one or more of the steps of the method1100, and the program may comprise program instructions stored on acomputer readable memory or programmed steps of the logic circuitry, forexample.

While preferred embodiments of the present invention have been shown anddescribed herein, it will be obvious to those skilled in the art thatsuch embodiments are provided by way of example only. Numerousvariations, changes, and substitutions will now occur to those skilledin the art without departing from the invention. It should be understoodthat various alternatives to the embodiments of the invention describedherein may be employed in practicing the invention. It is intended thatthe following claims define the scope of the invention and that methodsand structures within the scope of these claims and their equivalents becovered thereby.

1.-2. (canceled)
 3. A system for planning an orthodontic treatment, thesystem comprising: a processor; and a memory operably coupled to theprocessor and storing instructions that, when executed by the processor,cause the system to perform operations comprising: receiving a digitalrepresentation of an initial position of a tooth of a patient,determining a target position for the tooth, determining anovercorrected position for the tooth that is different from the targetposition, wherein the overcorrected position is determined based on anovercorrection matrix generated from clinically-determined relationshipsbetween planned tooth movements and achieved tooth movements, andoutputting fabrication instructions for an orthodontic applianceincluding an overcorrected tooth receiving cavity corresponding to theovercorrected position for the tooth.
 4. The system of claim 3, whereinthe overcorrection matrix is generated by inverting an achievementmatrix representing the clinically-determined relationships between theplanned tooth movements and the achieved tooth movements.
 5. The systemof claim 3, wherein the overcorrected position is one or more oftranslated or rotated relative to the target position.
 6. The system ofclaim 3, wherein the operations further comprise determining a movementvector between the initial position and the target position.
 7. Thesystem of claim 6, wherein the movement vector includes a translationalcomponent, and the operations further comprise adding a rotationalcomponent to the translational component.
 8. The system of claim 7,wherein the rotational component is configured to compensate for atipping effect.
 9. The system of claim 7, wherein determining theovercorrected position comprises modifying the movement vector using theovercorrection matrix.
 10. The system of claim 3, wherein theovercorrected position is determined based on a plurality ofcorrelations between teeth movements and force systems.
 11. The systemof claim 3, wherein the overcorrected tooth receiving cavity isconfigured to apply one or more forces to the tooth to cause the toothto move from the initial position to an actual position different fromthe overcorrected position.
 12. The system of claim 3, wherein theoperations further comprise limiting the overcorrected position based onone or more of a minimum vertex distance or a maximum vertex distance.13. The system of claim 3, wherein the orthodontic appliance is apolymeric shell appliance including a plurality of teeth receivingcavities.
 14. A system for planning an orthodontic treatment, the systemcomprising: a processor; and a memory operably coupled to the processorand storing instructions that, when executed by the processor, cause thesystem to perform operations comprising: receiving a digitalrepresentation of an initial position of a tooth of a patient,determining a target position for the tooth, generating a movementvector corresponding to movement of the tooth from the initial positionto the target position, determining an overcorrected movement vectorbased on an overcorrection matrix generated from clinically-determinedrelationships between planned tooth movements and achieved toothmovements, and outputting fabrication instructions for an orthodonticappliance including an overcorrected tooth receiving cavity configuredto apply a force system to the tooth corresponding to the overcorrectedmovement vector.
 15. The system of claim 14, wherein the overcorrectedmovement vector is determined by multiplying the movement vector withthe overcorrection matrix.
 16. The system of claim 14, wherein theovercorrection matrix is generated by inverting an achievement matrixrepresenting the clinically-determined relationships between plannedtooth movements and achieved tooth movements.
 17. The system of claim14, wherein the movement vector includes a translational component, andthe overcorrected movement vector includes a combination of thetranslational component and a rotational component.
 18. The system ofclaim 17, wherein the rotational component is configured to compensatefor a tipping effect.
 19. The system of claim 14, wherein theovercorrected movement vector is configured to move the tooth from theinitial position to an overcorrected position different from the targetposition.
 20. The system of claim 19, wherein the force system isconfigured to cause the tooth to move from the initial position to anactual position different from the overcorrected position.
 21. Thesystem of claim 14, wherein the operations further comprise limiting theovercorrected movement vector based on one or more of a minimum vertexdistance or a maximum vertex distance.
 22. The system of claim 14,wherein the orthodontic appliance is a polymeric shell applianceincluding a plurality of teeth receiving cavities.